Mobile-Assisted Localization in Sensor Network

1. Mobile-Assisted Localization in Sensor Network Charles Zha CSE 590 Fall 2005

2. Agenda • Challenge of Current Localization Methods • Mobile-Assisted Localization (MAL) Strategy • Optimization Using Anchor-Free Localization (AFL) • MAL Performance Evaluation • Conclusion

3. Localization Challenges In Reality • Obstructions • Lack of line-of-sight connectivity prevents the nodes to obtain pairwise distance • Sparse Node Deployments • Not always possible to obtain rigid structure and unique solution • Geometric Dilution of Precision (GDOP) • May incur large errors in estimation and measurements if a node is far from the group

4. Mobile-Assisted Localization • Find four stationary nodes • Using Specific MAL Movement Strategy To Construct A Rigid Graph And Compute Inter-node Distance • Using Anchor-Free Localization to Compute Coordinates and Optimize Solution

5. Why 7 mobile positions are sufficient? • Calculating distances among 4 (or more) nodes To compute the pairwise distances between j>=4 nodes n1,n2,….,nj We require at least [(3j-5)/(j-3)] mobile positions (to reduce the degree of freedom to 0) When j=4, the [(3j-5)/(j-3)]=7

6. MAL Movement Strategy • Initialize: • Find Four Stationary Nodes that are visible (distance are measurable) to mobile location s s s s v

7. MAL Movement Strategy • Initialize: • Move the mobile to at least seven nearby locations and measure distances v v v s s v s v s v v

8. MAL Movement Strategy • Initialize: • Compute the pairwise distances between the four stationary nodes v v v s s v s v s v v

9. MAL Movement Strategy • Initialize: • Localize the resulting tetrahedron using Rigidity Theorem v v v s s v s v s v v

10. MAL Movement Strategy • Loop: • Pick a stationary node that has been localized but has not yet examined by this loop • Move the mobile around the stationary node and search for non-localized stationary node and 0,1 or 2 additional localized nodes • For each such mobile position: Compute the distance between those 2,3,or 4 stationary nodes and localize the node if it has 4 know distances. • Terminates the loop if every stationary node has been localized or no more progress can be made.

11. Why Anchor-Free Localization? • Most localization algorithms are designed for well-connected dense networks with relatively small obstacles. • AFL does specially well for network with large obstacles (indoors) and low connectivity, where MAL can be very helpful.

12. Anchor-Free Localization Algorithm • Initialization Phrase: • Computes an initial coordinate assignment for nodes • Runs multiple instances of Leader election algorithm to elect certain of nodes • Uses shortest path hop count to compute the initial coordinates of each node

13. Anchor-Free Localization Algorithm For two nodes i,j, let hi,j denote the shortest path hp count, and let R denote the “range” of the nodes

14. Anchor-Free Localization Algorithm • dm(i,j) is the distance between nodes i and j obtained by MAL. And because MAL produces rigid graph, E=0. dm(i,j) is an approximation to di,j , the coordinate assignment to the global minimum E results in graph that approximates the true embedded graph. • AFL uses a non-linear optimization algorithm to minimize the sum-squared energy E of the graph defined by:

15. MAL Performance Evaluation Coordinates obtained by MAL after running the AFL optimization.

16. MAL Performance Evaluation • Error decreases as number, coverage of reference nodes increase, and mobile positions increase.

17. Conclusion • Easier to get around Obstructions by moving around • Easier to construct rigid graph to obtain unique solution • Smaller distance estimation errors, especially with larger mobile coverage area